Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2002-06-06
Physics
Condensed Matter
Disordered Systems and Neural Networks
13 pages, Revtex file, 8 postscript files. It will appear in the special edition of J. Phys. A for Random Matrix Theory
Scientific paper
10.1088/0305-4470/36/12/322
We describe the singularities in the averaged density of states and the corresponding statistics of the energy levels in two- (2D) and three-dimensional (3D) chiral symmetric and time-reversal invariant disordered systems, realized in bipartite lattices with real off-diagonal disorder. For off-diagonal disorder of zero mean we obtain a singular density of states in 2D which becomes much less pronounced in 3D, while the level-statistics can be described by semi-Poisson distribution with mostly critical fractal states in 2D and Wigner surmise with mostly delocalized states in 3D. For logarithmic off-diagonal disorder of large strength we find indistinguishable behavior from ordinary disorder with strong localization in any dimension but in addition one-dimensional $1/|E|$ Dyson-like asymptotic spectral singularities. The off-diagonal disorder is also shown to enhance the propagation of two interacting particles similarly to systems with diagonal disorder. Although disordered models with chiral symmetry differ from non-chiral ones due to the presence of spectral singularities, both share the same qualitative localization properties except at the chiral symmetry point E=0 which is critical.
Evangelou S. N.
Katsanos D. E.
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